If the vectors (6, 4) and (3, m) are perpendicular, what is the value of m?

Let $\vec{v_1} = (6, 4)$ and $\vec{v_2} = (3, m)$.

The dot product of $\vec{v_1} = (x_1, y_1)$ and $\vec{v_2} = (x_2, y_2)$ is $x_1 x_2 + y_1 y_2$.
Since the vectors are perpendicular, their dot product is 0:

The final answer is $-\frac{9}{2}$.